Find the diameter of the semicircle inscribed in ABC, whose diameter lies on AB, and that is tangent to AC and BC.

Question

In triangleABC, side AB = 20, AC = 11, and BC = 13. Find the diameter of the semicircle inscribed in ABC, whose diameter lies on AB, and that is tangent to AC and BC.

Answer 1

Answer : 11

1/2*r*11 + 1/2*r*13 = [s(s-a)(s-b)(s-c)]^1/2

where s = (a+b+c)/2 = 22

1/2*r*24 = [22*2*11*9]^1/2 = 66
r = 66/12 = 11/2
Diameter = 11